I ; 


EXCHANGE 


Are  Electrolytes  Completely  Ionized 
at  Infinite  Dilution? 


DISSERTATION 

Submitted  in  Partial  Fulfillment  of  the  Requirements  for  the 

Degree  of  Doctor  of  Philosophy  in  the  Faculty 

of  Pure  Science,  Columbia  University 

in  the  City  of  New  York. 


BY 


Harold  E.  Robertson,  A.  B. 


NEW  YORK  CITY 
1921 


Are  Electrolytes  Completely  Ionized 
at  Infinite  Dilution? 


DISSERTATION 

vSubmitted  in  Partial  Fulfillment  of  the  Requirements  for  the 

Degree  of  Doctor  of  Philosophy  in  the  Faculty 

of  Pure  Science,  Columbia  University 

in  the  City  of  New  York. 


BY 

Harold  E.  Robertson,  A.  B. 


NEW  YORK  CITY 
1921 


TO 
MY  FATHER  AND  MOTHER 


ACKNOWLEDGMENT 

It  is  with  great  pleasure  that  I  express  my  sincere 
appreciation  of  the  constant  advice  and  assistance  of 
Professor  Harold  A.  Fales  under  whose  direction  this 
work  was  carried  to  completion. 


ARE  ELECTROLYTES  COMPLETELY  IONIZED 
AT  INFINITE  DILUTION? 

Ever  since  the  acceptance  of  the  ionic  theory  put  forward  by 
Arrhenius  *  one  of  the  most  fundamental  questions  has  been  the  degree 
of  ionization  of  electrolytes  at  infinite  dilution.  The  idea  generally  held 
at  present,  as  a  result  of  extensive  investigations  by  means  of  conductiv- 
ity measurements,  is  that  as  we  approach  infinite  dilution,  the  degree  of 
ionization  approaches  unity. 

However  there  are  several  objections  to  the  conclusions  which  have 
been  drawn  fiom  conductivity  data.  These  objections  have  partly  to  do 
with  the  measurements  themselves,  and  partly  with  their  interpretation. 
With  respect  to  the  former  we  may  mention  principally  that  it  is  not  prac- 
ticable without  using  apparatus  of  extreme  complexity  2  to  make  meas- 
urements at  dilutions  3  in  excess  of  one  thousand  liters  per  mol  because 
of  the  relatively  enormous  errors  which  are  introduced  by  the  presence 
of  the  merest  traces  of  impurities  in  the  solution  being  measured ;  with 
respect  to  the  latter  we  may  mention,  first  the  uncertainty  which  exists 
as  to  the  water  correction  which  must  be  applied,  and,  secondly  the  fact 
that  the  value  of  the  equivalent  conductivity  at  infinite  dilution  A04,  i§ 
obtained  not  by  direct  experiment  but  by  extrapolation  from  measure- 
ments of  A  stopping  at  the  lower  limit  of  A0.ooi-  Among  the  numerous 
formulae  for  making  this  extrapolation  the  ones  which  have  been  em- 
ployed most  frequently  are  those  due  to  Kohlrausch5,  Noyes6,  Storch7, 
Kraus  and  Bray8,  Kendall9,  and  Washburn10.  A  complete  discussion  of 
the  various  methods  of  calculation  and  the  errors  incident  thereto  is  given 
by  Bates11. 

1  Z.  Physik.  Chem.  1,  631  (1899). 

2  Washburn,  J.  Amer.  Chem.  Soc.  40,  122  (1918). 

3  The  term  dilution  as  used  here  means  the  number  of  liters  of  solution  con- 
taining one  mol  of  solute. 

4  This  is  also  called  AOQ  . 

5  Wiss.  Abh.  Phys.  Tech.  Reichanstalt.  3,  155  (1900). 
Sitzunber,  konigl.  preuss.  Akad.  (1900). 

Z.  Elektrochem.  13,  333  (1907). 

6  Pub.  Car.  Inst.  63,  337  (1907). 
^Z.  Physik.  Chem.  19,  13  (1896). 

Bancroft,  ibid.,  31,  188  (1899). 
8J.  Amer.  Chem.  Soc.  35,  1315  (1915). 

9  Trans.  Chem.  Soc.,  101,  1275  (1912). 

10  loc.  cit. 

11  J.  Amer.  Chem.  Soc.  35,  519  (1913). 


The  curve  given  below  in  Fig.  I  illustrates  the  method  followed  by 


Noyes1 


in    determining 
1 


The    equation    used    by    this    author    is 


1         1 

—  =  —  -f  K(O)11-1,  —  being  plotted  against 


n~l  and  n  being  varied 


until  the  nearest  approach  to  a  straight  line  is  obtained.  The  dotted  por- 
tion of  the  curve  shows  the  extrapolation  for  n  =  1.45.  The  data  is  taken 
from  the  section  of  Noyes'  work  on  hydrochloric  acid  at  18°  ;  it  is 
(Table  I)  : 

TABLE  I 


Cone.  HC1. 

0.0005  M 
.002 
.01 
.08 
.10 


26.7 

(n  =  1.45) 
0.47 

(CA)n-i 
(n  =  1.40) 
0.50 

26.8 

0.857 

0.89 

27.2 

1.84 

1.69 

28.2 

4.50 

3.73 

28.5 

4.84 

4.15 

FIG  I 


HYDROCHLORIC  _ 
ACID 
18° 


2 

CCA) 

Putting  this  same  data  in  somewhat  different  form  and  plotting  de- 
gree of  ionization  against  the  logarithm  of  dilution  in  order  to  show  the 
assumed  approach  to  complete  ionization  with"  increasing  dilution  as 
extrapolated  from  conductivity  measurements  we  get  the  data  of  Table 
II  and  the  curve  given  in  Fig  II. 


1  loc.  cit. 


Conc.HCl. 
0.1 
0.08 
0.01 

0.002 
0.0005 


TABLE   II 

Log.  of  Dilution 
1.0 
1.1 
2.0 
2.7 
3.3 


Percentage  lonization 
92.5 
93.5 
97.1 
98.6 
99.0 


FIG. II 


NTAGE  -  lONIZATION  (BY  CONDUCTIVITY 

CO  CD  CO  CO  o 

ro  _k».  o  oo  o 

s 

"•^ 

fyj^MOV 

/H  FORTH 

S  REGION 

/ 

< 

/ 

HYDROl 

:HLORI 

C    ACI 

),  18° 

4 

/ 

i 

o 


0          I          234567 
LOG  OF  NUMBER  or  LITERS  CONTAINING  1  MOL 


In  view  of  the  preceding  considerations  it  would  seem  highly  desir- 
able to  bring  to  bear  some  independent  method  of  investigation  in  regard 
to  the  behavior  of  the  ionization  of  electrolytes  in  the  region  under  dis- 
cussion. Such  a  method  seems  to  be  present  in  the  electromotive  method 
of  Nernst1  for  the  measurement  of  ionic  concentrations,  and  it  may  be 
pertinently  mentioned  here  that  this  method  for  the  region  under  consid- 
eration is  free  from  the  experimental  difficulties  which  seem  to  render 
the  conductivity  method  of  slight,  if  any,  avail ;  thus  the  presence  of 
slight  impurities  derived  by  the  solutions  either  from  their  containing 
vessels  or  the  air  have  no  appreciable  effect  on  the  e.m.f.  measurements, 
and  further  the  enormous  specific  resistance  of  the  solutions  being  meas- 
ured is  no  obstacle  if  the  ballistic  galvonometer  is  employed  in  place  of 
the  potentiometer  according  to  the  method  described  by  Beans  and 
Oakes2. 


iZ.  Physik.  Chem.  4,  129  (1889). 

2  J.  Amer.  Chem.  Soc.  42,  2116  (1920). 


Because  of  the  large  amount  of  work  that  has  been  done  on  acids  it 
was  thought  well, by  the  present  author  to  investigate  the  several  types 
of  acids :  monobasic,  dibasic,  and  tribasic,  and  accordingly  hydrochloric, 
acetic,  sulfuric  and  phosphoric  acid  solutions  were  made  up  in  dilutions 
ranging  from  ten  liters  per  mol  to  three  million  liters  per  mol.  The  con- 
centration of  hydrogen  ion  was  calculated  from  the  e.m.f.  measurements 

CH+       i 
by  means  of  Nernst's  formula  e  —  .000198  T  log  -  -  .     The  value 

KVpH2 

so  obtained  for  C  H+  was  multiplied  by  one  hundred  and  divided  by  the 
total  concentration  of  acid  present  times  the  valence  of  the  anion.  The 
quotient  of  this  division  is  what  we  will  call  the  thermodynamic  percent- 
age ionization.2  The  surprising  fact  is  that  the  values  so  obtained  rise 
generally  to  a  maximum  and  then  fall  off  rapidly  toward  zero  as  the  dilu- 
tion increases,  cf.  Fig.  IV. 

EXPERIMENTAL   METHOD 

Water  Bath 

To  prevent  electrical  leaks  the  cells  were  immersed  in  an  oil  bath 
which    was    placed    in    a    large    water    bath    electrically    regulated    to 
25°  C±0.01°. 
Cells 

The  following  e.m.f.  combination  was  employed : 
Hg— HgCl  sat.  KC1  —  sat.  KC1  —  Hx  —  Hx  —  H,  ( 1  atmos.)  Pt.3 
The  saturated  calomel  cell  as  described  by  Fales  and  Mudge  *  was  used 
throughout  this  work,  likewise  the  hydrogen  cells,  electrodes  and  purify- 
ing train  for  the  hydrogen.    The  hydrogen  cells  were  steamed  out  before 
each  series  of  determinations  and  the  electrodes  were  also  thoroughly 
boiled  with  distilled  water.    To  determine  whether  the  dissolving  of  ma- 
terials from  the  hydrogen  electrode  cells  would  be  appreciable,   some 
conductivity  and  e.m.f.  measurements  were  simultaneously  taken.     The 

1  In  this  formula,  "e"  represents  the  pole  potential  2C  H+  in  volts,  "T"  =  abso- 
lute temperature,  logarithms  are  to  the  base  10,  CH+  is  in  mols  per  liter,  "K"  is  the 
solution  tension  constant,  pH2  is  the  partial  pressure  of  the  hydrogen  in  atmos- 
pheres. 

2  It  seems  desirable  to  follow  the  lead  of  M.  C.  McC.  Lewis,  Proc.  Chem.  Soc. 
117,  1120  (1920)  and  call  the  hydrogen  ion  concentration  as  calculated  from  e.m.f. 
measurements  by  Nernst's  formula  the  thermodynamic  concentration  of  hydrogen 
ion,  hence  by  a  simple  extension  of  this  term  we  deduce  the  term  "thermodynamic 
ionization."    This  is  what  G.  N.  Lewis,  J.  Amer.  Chem.  Soc.  35,  1  (1913),  calls  the 
activity  of  the  hydrogen  ion. 

3  The  symbol  Hx  represents  the  acid  being  used, 
4J.  Amer.  Chem.  Soc.  42,  2434  (1920). 


solution  measured  was  0.0000005  M.  sulfuric  acid.  The  fresh  solution 
was  placed  in  the  hydrogen  cell  and  the  hydrogen  passed  for  varying 
lengths  of  time  with  the  results  given  in 

TABLE   III 

Time                               Specific  Conductivity  Observed 

mhos.  e.m.f.  volt 

0                                              2.12  X  10-fi  .6352 

\l/2  hr.                                      4.08  X  10-6  .6352 

2H  hr.                                       4.11  X  HH  .6352 

2  weeks                                   1.56  X  1(H  .6350 

It  would  seem  from  this  that  the  effect  of  dissolving  any  impurities 
from  the  cells  may  be  considered  negligible,  especially  as  the  voltage  was 
constant  and  reproducible  regardless  of  the  time  that  the  solution  was 
in  the  cell. 

Liquid  Junctions 

Reproducible  results  were  obtained  by  using  cotton  plugs.1  To  pre- 
vent contamination  of  the  solution  being  measured  a  double  salt  bridge 
was  used.  One  beaker  contained  saturated  potassium  chloride  into  which 
calomel  cell  dipped.  The  other  beaker  contained  the  solution  being  meas- 
ured and  the  goose-neck  siphon  hydrogen  cell  dipped  into  this.  Connec- 
tion between  the  two  beakers  was  made  by  a  siphon  tube  of  internal 
diameter  of  about  0.5  cm.,  plugged  writh  cotton  wool  and  containing  the 
.solution  being  measured.  This  method  gave  very  constant  and  repro- 
ducible results,  the  voltage  of  the  system  remaining  practically  constant 
for  several  hours  after  the  solution  and  electrode  had  become  saturated 
with  hydrogen. 

Preparation  of  Materials  and  Solutions 

Conductivity  water  was  used  in  making  up  the  solutions,  as  used, 
the  water  had  a  specific  conductivity  at  25°  of  about  1.7  X  1O"6  mhos.; 
its  content  of  ammonia  was  0.5  mg.  (3  X  10~8  mol)  of  NH3  per  liter  2 ; 
when  tested  electrometrically  in  combination  (I)  at  sundry  times,  the 
observed  voltages  for  the  portions  tested  lay  between  0.660  and  0.680  volt. 
The  mercury  used  in  the  calomel  cells  was  purified  by  washing  several 

1  Fales  and  Mudge,  loc,  cit. 

2  Whether  this  ammonia  is  present  as  ammonium  hydroxide  or  some  ammonium 
salt  is  a  question  which  can  not  be  settled  experimentally.    Judging  from  the  work 
of  Kendall,  J.  Amer.  Chem.  Soc.  38,  1480  (1916),  who  offers  evidence  to  show  that 
conductivity  water  in  contact  with  the  air  has  a  content  of  CO2  of  1.4  X  1^~5  mols 
per  liter  and  from  the  work  of  Paine  and  Evans,  Proc.  Camb.  Phil,  Soc.,  (1)   18, 
1    (1914),  on  the  conductivity  of  dilute  solutions  of  sulfuric  acid  containing  very 
small  amounts  of  ammonium  carbonate,  it  would  seem  a  reasonable  premise  that 
the  ammonia  is  present  as  ammonium  carbonate. 


10 

times  in  nitric  acid  by  the  method  of  Hildebrand  1t  filtering  through  a 
dry,  clean  towel  and  distilling  under  reduced  pressure  according  to  the 
method  of  Hulett.2 

The  potassium  chloride  used  in  the  cells  was  a  c.p.  analyzed  sample, 
twice  recrystallized  from  water  and  then  fused  in  platinum.  For  the  salt 
bridge  the  analyzed  sample  was  used  without  purifying.  The  calomel  for 
the  cells  was  a  c.p.  analyzed  sample  of  such  grade  as  had  been  found  by 
by  Fales  and  Mudge  3  to  give  satisfactory  results.  The  hydrochloric 
acid  was  purified  by  diluting  a  12  molar  sloution  of  a  c.p.  analyzed  sam- 
ple with  an  equal  volume  of  water,  distilling  and  collecting  the  middle 
portion.  The  acetic,  sulfuric  and  phosphoric  acids  were  c.p.  analyzed 
materials  used  as  obtained.  All  solutions  were  made  up  at  25°.  The 
hydrochloric  and  acetic  acids  were  each  made  up  to  a  concentration  of 
0.1  M.,  the  sulfuric  acid  0.05  M.,  and  the  phosphoric  0.0333  M.4 ;  these 
stock  solutions  were  kept  in  "Non-Sol"  bottles,  which  had  been  well 
steamed  out.  The  weaker  solutions  were  made  up  as  required  by  diluting 
the  stock  solutions  for  concentrations  ranging  down  to  0.001  M.  For  the 
more  dilute  solutions  a  0.001  M.  stock  solution  was  used  and  dilutions 
made  from  this.  All  dilutions  were  made  at  25°  using  standard  flasks 
and  pipettes  calibrated  at  25°  and  all  solutions  were  kept  in  Non-Sol 
bottles. 

Gal  vono  meter 

The  galvonometer  which  was  of  the  ballistic  type,  had  the  following 
characteristics:  a  sensitivity  of  9090  megohms,  a  period  of  21.4  seconds 
and  a  critical  resistance  of  35,000  ohms ;  the  scale  was  50  cm.  from  the 
galvonometer's  mirror.  The  condenser  was  a  standard  mica  instrument 
with  steps  of  0.001  microfarad  to  0.5  microfarad  and  a  total  capacity  of 
one  microfarad.  It  was  carefully  calibrated  in  the  Ernest  Kempton  lab- 
oratory, Department  of  Physics,  Columbia  University  and  found  to  be 
correct.  For  charging  and  discharging  the  condenser  a  key  having 
double  contacts  and  mounted  on  hard  rubber- was  used.  The  several  in- 
struments, galvonometer,  condenser,  and  key  were  set  on  rubber  stoppers 
and  all  wires  were  run  on  insulators  and  all  connections  soldered.  As  a 
primary  standard  fo  e.m.f.  a  Weston  standard  cell  was  used ;  this  had 

1  J.  Amer.  Chem.  Soc.  31,  933  (1909). 

2  Z.  Physik.  Chem.  33,  611  (1900). 
a  loc.  cit. 

4  The  hydrochloric  and  sulfuric  acids  were  standardized  by  titration  against 
pure  sodium  carbonate  using  methyl-orange  as  indicator.  Tenth  molar  sodium 
hydroxide  was  standardized  against  the  hydrochloric  acid  and  used  for  the  stand- 
ardization of  the  acetic  acid,  using  phenolphthalein  as  indicator.  The  phosphoric 
was  standardized  gravimetrically  using  magnesia  mixture  as  the  precipitant  and 
igniting  the  precipitate  to  magnesium  pyrophosphate. 


11 

an  e.m.f.  of  1.0183  volts  at  20°  as  was  verified  by  checking  against  two 
other  standard  cells  which  had  been  certified  by  the  U.  S.  Bureau  of 
Standards. 

Calibration 

The  electromotive  forces  measured  in  this  work  ranged  from  0.3  to 
07  volts.  The  galvonometer  was  calibrated  by  taking  various  voltages  x 
in  this  range  and  reading  the  deflection  for  the  capacities,  0.10,  0.15,  0.20, 
0.25,  0.30,  of  a  microfarad.  For  each  capacity  a  constant  was  obtained 


1.100  r 


1.000 


FIG.H 


4          6          8          10         12 

DEFLECTION  (CM.) 


14 


16 


1  The  voltages  used  for  this  calibration  were  obtained  by  using  phosphate  and 
citrate  buffers  according  to  Clark,  "The  Determination  of  Hydrogen  Ions,"  Wil- 
liams and  Wilkins,  Baltimore,  1920,  page  68.  The  e.m.f.  of  these  solutions  were 
first  measured  on  the  potentiometer  and  then  readings  taken  on  the  ballistic  gal- 
vonometer. 


12 

by  dividing  the  voltage  by  the  deflection  in  scale  divisions,  graduated  in 
centimeters.  This  is  shown  graphically  in  Fig.  Ill,  where  voltage  is 
plotted  as  the  ordinate  against  deflection  as  the  abscissa,  a  straight  line 
resulting  for  each  capacity.  This  procedure  tends  to  minimize  any  errors 
due  to  irregularities  in  the  scale  or  condenser.2 

The  calibration  of  the  ballistic  galvonometer  could  be  checked  when- 
ever desired  by  using  the  standard  Weston  cell  and  an  appropriate  capac- 
ity. Observations  taken  throughout  the  course  of  the  work  showed  that 
the  total  deflection  for  any  given  capacity  and  e.m.f.  was  constant,  al- 
though the  zero  point  of  the  galvonometer  often  shifted  slightly,  ±  0.1 
cm.,  from  reading  to  reading.  As  a  further  check,  during  routine  meas- 
urements an  e.m.f.  was  first  determined  by  the  ballistic  galvonometer  and 
then  on  the  potentiometer,  or  by  the  standard  cell  using  the  ratio, 
Estd  :  Ex:  :  Defstd  :  Defx  ,  where  Estd  is  the  e.m.f.  of  the  standard  cell, 
Defgtd  is  the  corresponding  deflection  on  the  ballistic  galvonometer,  and 
Ex  and  Defx  have  a  similar  significance  for  the  unknown  cell.  These 
methods  gave  checks  within  —  0.5  milivolt. 

It  was  found  necessary  to  choose  the  capacity  used  in  any  given  meas- 
urement so  that  the  deflection  read  was  between  10  and  15  cm.  If  the 
readings  were  more  than  15  cm.  the  results  are  too  low,  as  the  observed 
readings  are  not  then  directly  proportional  to  the  tangent  of  the  angle ; 
if  less  than  10  cm.  then  the  precision  is  too  low.  Under  these  restrictions 
the  method  is  accurate  to  0.5  milivolt  as  the  deflection  of  the  ballistic  gal- 
vonometer can  be  read  to  ±  0.2  mm. 

The  apparatus  was  tested  for  electrical  leaks  as  follows :  The  con- 
denser was  charged  by  means  of  the  standard  cell,  this  operation  taking 
from  one  to  two  minutes ;  it  was  then  immediately  discharged  through 
the  ballistic  galvonometer  and  the  deflection  noted ;  the  condenser  was 
again  charged  ;  disconnected  from  the  standard  cell  by  means  of  a  switch, 
allowed  to  stand  from  five  to  ten  minutes,  and  then  discharged  through 
the  galvonometer  and  the  deflection  noted.  On  clear  days  the  difference 
between  these  two  deflections  was  about  one  centimeter  for  a  deflection 
of  12  cm.,  so  that  on  clear  days  the  leakage  for  an  immediate  discharge 
of  the  condenser  was  negligible.  On  days,  however,  when  the  humidity 
was  high  the  leakage  was  very  rapid  for  if  under  these  conditions  the 
condenser  was  charged  and  allowed  to  stand  only  thirty  seconds  before 
discharging,  the  deflections  would  often  be  five  or  six  centimeters  differ- 
ent from  that  obtained  from  an  immediate  discharge  of  the  condenser, 

1  In  making  a  determination  the  solution  whose  concentration  of  hydrogen  ion 
was  to  be  determined  was  placed  in  the  e.m.f.  combination  shown  above,  a  cer- 
tain capacity  taken,  the  deflection  read  on  the  ballistic  galvonometer  and  this  read- 
ing multiplied  by  the  constant  for  that  capacity  in  order  to  give  the  observed  e.m.f. 


13 

sometimes  being  greater,  sometimes  less.  In  consequence  of  the  preced- 
ing observations  the  practice  was  always  followed  of  making  readings 
only  on  clear  days ;  and  it  may  be  accepted  with  respect  to  the  recorded 
results  of  this  paper  that  the  error  due  to  the  electrical  leakage  is  in  any 
case  not  greater  than  what  corresponds  to  a  deviation  of  ±0.1  mm.  in  the 
galvonometer  reading. 

EXPERIMENTAL  RESULTS 

The  data  obtained  for  the  four  different  acids  is  given  in  the  follow- 
ing tables,  Nos.  IV,  V,  VI,  and  VII.  In  each  table  the  first  column  gives 
the  molarity  of  the  acid  used ;  the  second  gives  the  observed  electromo- 
tive force  of  the  system  measured  (see  page  8) ;  the  third  gives  the  ther- 
modynamic  concentration  of  hydrogen  ion  as  calculated  by  Nernst's 

c  H+   x  100 

formula1,  the  fourth  gives  the  ratio  — —  -,  which  in 

Cacid    X  valence  of  anion 

other  words  is  the  percentage  ionization  based  on  the  thermodynamic 
concentration  of  hydrogen  ion.  In  the  curves,  Fig.  IV,  the  values  of  col- 
umn four  are  plotted  as  ordinates  against  the  logarithm  of  the  number  of 
liters  containing  one  mol  of  acid  as  abcissa.  Each  value  is  the  mean  of 
at  least  four  determinations  made  on  separate  samples  at  different  times, 
and  for  each  value  at  least  five  readings  of  the  galvonometer  were  taken 
over  an  interval  of  time  from  an  hour  to  three  hours  or  until  they  were 
constant. 

1  In  making  these  calculations  the  value  of  K  in  Nernst's  formula  was  taken 
as  lO-4-70  while  the  value  of  the  contact  potential  between  the  saturated  KC1  salt 
bridge  and  the  acid  being  employed  was  assumed  to  be  zero.  (For  the  validity  of 
assumption  just  mentioned  see  the  caption  under  Discussion  entitled  Contact 
Potential.) 

An  alternative  method,  identical  in  principle  and  effect  with  the  foregoing,  is  to 

0.2488  —  E  obs 

use  the  relationship  log  C  TT+  = which  is  obtained  by  re-arrange- 

0.059.11 

CH+ 

Q 

ment  of  the  expression  E0  —  E0ks  =  0.05911   log ,  where  E0  is  the  e.m.f.  of 

CH+x 

the  system  Hg— HgCl  sat.  KC1  —  0.1   M.  HC1  —  H2   (1  Atmos)   Pt.  for  25°  and 

has  the  value  of  0.3100  volt  (cf.  Fales  and  Mudge,  loc.  cit.),  Cjj+     is  the  concentra- 

o 
tion  of  hydrogen   ion   in   0.1    M.   HC1   at  25°    and   as   determined   by   conductivity 

methods  has  the  value  0.09204  M.,  Eobs  is  the  observed  e.m.f.  obtained  by  the  use 
of  combination  (I). 


Cone,  of  acid 

0.10  M 

0.01 

0.005 

0.001 

0.0001 

0.00005 

0.00002 

0.00001 

0.000005 

0.000001 


14 

TABLE  IV 
Hydrochloric  Acid 


e.m.f.  Obs. 


CH+   X  100 


-^  XJ.  ' 

C  acid   X  1 

0.3100 

9.204  X  10-2 

92.0 

.3657 

1.053  X  10-2 

105.3 

.3820 

5.580  X  10-3 

111.6 

.4225 

1.152  X  10-3 

115.2 

.4824 

1.117  X  10-4 

111.7 

.5011 

5.390  X  10-5 

107.8 

.5272 

1.950  X  10-5 

97.9 

.5521 

7.394  X  10-6 

73.9 

.5804 

2.455  X  10-6 

49.1 

.6376 

2.644  X  10-7 

26.4 

TABLE  V 
Acetic  Acid 


Cone,  of  acid 

0.05  M 

0.005 

0.001 

0.0002 

0.0001 

0.00005 

0.00001 

0.000005 

0.000001 


e.m.f.  Obs. 

.4210 
.4495 
.4716 
.4979 
.5077 
.5219 
.5710 
.6104 
.6545 


CH+ 

1.221  x  1<H 

4.24    X  10-4 

1.701  X  10-* 

6.107  X  10-5 

4.169  X  10-5 

2.398  X  10-3 

3.540  X  10-6 

7.630  X  10-7 

1.370  X  10-7 


CH+  X100 

Cacid      XI 

2.44 

8.05 
17.01 
30.5 
41.7 
47.95 
35.4 
15.3 
13.7 


Cone,  of  acid 

0.05  M 

0.005 

0.001 

0.0005 

0.00005 

0.00001 

0.000005 

0.0000005 


TABLE  VI 
Sulfuric  Acid 


e.m.f.  Obs. 


CH+   X100 


V  XX  ' 

Cacid   X2 

.3174 

6.802  X  10-2 

68.0 

.3698 

8.974  X  10-3 

89.7 

.3852 

4.926  X  10-3 

98.5 

.4255 

1.025  X  10-3 

102.5 

.4866 

9.484  X  10-5 

'94.8 

.5096 

3.872  X  10-5 

75.7 

.5602 

5.394  X  10-6 

53.9 

.6352 

2.904  X  lO-^ 

29.0 

15 

TABLE  VII 
Phosphoric  Acid 


nc.  of  a< 

0.0333 
0.00333 
0.00033 
0.00003 
0.00000 
0.00000 

120 
110 
100 
90 
o    80 

1    70 

0 

|60 
1    50 

DC 
LJ 

^   40 

LJ 

|   30 

z 

LJ 

cc    20 

LU 

CL- 
IO 

:id              e.m.f.  Obs.                   CH+ 

M                   .3582                    1.775  X  10~2 
.3983                   2.957  X  10~3 
3-                    .4517                   3.633  X  10~4 
33                   .5077                   4.169  X  10-3 
333                 .5766                   2.847  X  10~6 
333                 .6516                    1.533  X  10~7  ' 

FIG.E 

CH+    X  100 

Cacid      X3 

17.75 
29.57 
36.33 
41.69 
28.47 
1$.33 

s 

^N 

L 

/ 

( 

/    "^^^ 

: 

* 

/ 

A 

/ 

\\ 

/ 

r 

1 

\J 

T 

/ 

irJ. 

JLLO' 

.1-  HYDROCHLORIC  A 
I-  ACETIC 
I-SULFURIC 
BF  PHOSPHORIC 

25° 

CID 

I 

51 

I 

I 

/       * 
^'\\ 

•\ 

\\ 

/ 

.s'l 

\ 

/ 

/' 

1 

1 

!     -o    v  o 

\  M 

r^ 

A 

f/ 

\ 

\ 

\ 

] 

!.'''' 

,-* 

012345678 
LOG  OF  NUMBER  OF  LITERS  CONTAINING  1  MOL  SOLUTE. 


16 
DISCUSSION 

In  arriving  at  the  degrees  of  ionization  of  the  several  acids  under 
consideration,  Tables  IV  to  VII  inclusive,  three  assumptions  have  tac- 
itly been  made  and  it  consequently  becomes  necessary  to  consider  in  how 
far  these  assumptions  affect  the  validity  of  the  values  which  we  have  as- 
signed. The  three  assumptions  are :  that  the  contact  potential  between 
the  saturated  potassium  chloride  salt  bridge  and  the  solution  being  meas- 
ured is  zero ;  that  Nernst's  formula  for  pole  potential  differences  is  valid  ; 
that  the  ionization  of  the  respective  acids  is  unaffected  by  the  presence 
of  any  slight  impurities  that  might  have  been  present  in  the  solution. 

Contact  Potential 

As  to  the  manner  in  which  the  value  assigned  to  the  contact  poten- 
tial affects  the  results,  let  us  consider  the  particular  e.m.f.  system  which 
was  employed : 

Hg  —  HgClsat.  KC1  —  sat.  KC1  —  Hx  —  Hx  —  H2  (1  atmos.)  Pt. 
0.5266  zero  r          zero        e 

<-*  «^ 

It  can  be  seen  that  since  we  know  only  the  observed  value  of  the  system 
and  the  value  of  the  pole  potential  of  the  calomel  cell,1  we  can  not  arrive 
at  a  value  of  the  pole  potential  of  the  hydrogen  electrode  "e,"  until  we 
know  the  value  of  the  contact  potential  "r." 

As  a  matter  of  direct  experimentation  it  is  not  possible  to  determine 
"r"  but  from  the  indirect  experimentation  of  Fales  and  Vosburgh  ~  it 
would  seem  that  the  value  of  the  contact  potential  between  saturated 
potassium  chloride  and  1  M.  hydrochloric  acid  and  between  saturated 
potassium  chloride  and  0.1  M.  hydrochloric  acid  is  zero3;  and  inferen- 
tially  by  a  similar  process  of  reasoning  it  likewise  would  seem  that  the 
contact  potential  between  saturated  potassium  chloride  and  hydrochloric 
acid  solutions  of  less  concentration  than  0.1  M.  would  be  zero.  If  for 

1The  pole  potential  of  the  sat.  KC1  calomel  electrode  at  25°  is  equal  to  0.5266 
volt  on  the  basis  that  the  value  of  the  normal  calomel  cell  Hg  —  HgCl  1  M.  KC1  for 
18°  is  0.5600  volt  as  adopted  by  Ostwald,  Z.  Physik.  Chem.  35,  333  (1900),  cf.  Fales 
and  Mudge  (loc.  cit.).  Since  the  plus  or  minus  sign  attached  to  the  value  of  a  pole 
potential  difference  is  simply  to  indicate  the  e.m.f.  of  the  electrolyte  against  the 
electrode  and  leads  to  confusion  when  one  is  dealing  with  component  potential  dif- 
ferences of  a  combination,  it  is  preferable  to  make  use  of  arrows  to  indicate  the 
direction  in  which  the  positive  current  tends  to  flow  through  the  solution  by  virtue 
of  the  particular  potential  difference  involved. 

2  loc.  cit. 

3  This  is  also  assumed  by  W.  C.  McC.  Lewis,  loc.  cit. 


17 

such  latter  concentrations  we  approach  the  matter  entirely  on  theoretical 
grounds  by  means  of  Planck's  formula  l  for  contact  potential  difference 
we  can  arrive  at  some  estimate  of  limiting-  values  of  "r."  To  determine 
these  limiting  values,  complete  ionization  was  assumed  for  HC1  of  the 
following  concentrations,  and  calculations  2  made  accordingly  with  the 
following  results,  Table  VIII. 

TABLE  VIII 

Cone.  HC1  Mol  per  liter      0.01  0.001  0.0001  0.00001  0.000001 

Value  of  "r"  (volts)  0.0018  0.0018  0.0018  0.0018  0.0018 

These  potentials  are  directed  so  that  the  positive  current  tends  to 
flow  across  the  junction  from  the  acid  to  the  potassium  chloride.  If  we 
assume  the  respective  values  of  r  =  .0018,  instead  of  r  —  zero,  then  the 
value  which  we  would  assign  to  the  hydrogen  pole  potentials  from  the 
data  of  Tables  IV  to  VII  inclusive  would  be  correspondingly  greater,  and 
thus  larger  values  for  the  percentage  thermodynamic  ionization  would 
result  than  the  ones  given  in  said  tables. 

To  illustrate  these  considerations,  the  case  of  hydrochloric  acid  has 
been  taken  and  Table  IX  gives  in  the  first  column  the  concentration  of 


Cone.  HC1  e.m.f.  Obs. 


TABLE    IX 

CH+  X  100  CH+  X  100 


Cacid    x  1 

(r  =  0)  (r  =  .0018) 

0.01  M                         0.3657                       105.3  112.9 

.001                              .4225                       115.7  123.5 

.0001                             .4824                       111.7  119.8 

.00001                           .5521                         73.9  79.4 

.000001                         .6376                        26.4  28.4 

!Ann.  Phsik.  4,  581   (1890).    The  equation  is:    E  =  RT  log£  where  E  is  the 

contact  potential  difference  in  volts,  R  —  0.000198,  T  is  the  absolute  temperature 
and  |  is  a  transcendental  function  defined  by  the  equation  : 

€U2  —  Ut      log  c2/Cl-log£    £c2-c± 


Uj  is  the  sum  of  the  products  of  the  mobilities  of  the  positive  ions  in  the  dilute 
solution  times  their  respective  concentrations;  Vt  is  the  products  of  the  negative 
ions  in  the  dilute  solution  times  their  respective  concentrations  ;  c±  is  the  sum  of 
the  concentrations  of  the  positive  and  negative  ions  in  the  dilute  solution;  U2,  V2, 
and  c0  have  a  similar  significance  in  regard  to  the  concentrated  solution. 

-  The  method  of  calculation  was  that  given  by  Fales  and  kVosburgh,  loc.  cit., 
and  the  data  given  there  for  the  mobilities  of  the  ions  was  taken  for  these  calcula- 
tions ;  the  ionization  of  saturated  potassium  chloride  (4.1  M.)  at  25°  was  taken 
as  65%. 


18 

hydrochloric  acid  used,  in  the  second  the  observed  e.m.f.  of  the  combina- 
tion, in  the  third  the  percentage  thermodynamic  ionization  for  r  =  zero, 
and  in  the  fourth  the  same  for  r  =  0.0018  volt.1 

It  will  thus  be  seen  that  while  the  value  we  assign  to  the  contact  potential 
"r"  does  affect  the  values  we  get  for  the  thermodynamic  degree  of  ioniza- 
tion, it  will  still  be  true  for  each  separate  set  of  values  that  the  degree  of 
ionization  rises  to  a  maximum  and  then  falls  off  rapidly  toward  zero  as 
the  dilution  increases.  Compare  Figs  IV  and  V. 


FIG.Y 


01234567 
LOG  OF  NUMBER  OF  LITERS  CONTAINING  1  MOL.SOLUTE 


1  The  value  of  K  in  Nernst's  formula  was  taken  fo  rthese  calculations  as  KM-70. 


19 

Validity  of  Nernst  Formula  for  Pole  Potentials 

Nernst  1  in  deriving  his  general  formula  for  the  relationship  between 
pole  potential  and  ionic  concentration,  of  which  formula  the  one  em- 

CH+ 
ployed   on  page   8  of   this   article,  namely   e  =  .000198  T  log  - 


is  a  particular  form,  assumes  that  the  gas  laws  are  applicable  to  the  ion- 
ized portion  of  electrolytes  ;  or  in  other  words  that  the  osmotic  pressure  of 
the  ionised  portion  is  proportional  to  its  concentration.  Unfortunately 
we  have  no  direct  experimental  method  of  testing  this  assumption  al- 
though it  is  usually  taken  for  granted  that  it  applies  to  dilute  solutions, 
say  for  ionic  concentrations  not  greater  than  one-tenth  molar.  With  this 
restriction  as  to  the  concentration  of  electrolyte  it  may  be  remarked  that 
if  the  applicability  of  the  gas  laws  is  not  true  then  the  formula  will  have 
to  be  replaced  by  another  of  the  type 

CH> 
e  =  .000198  T  log.  -  -+f(CH+  ) 

KVpH2 

where  the  nature  of  the  function  f(CH+  )  would  have  to  be  determined. 
If  the  gas  laws  do  apply  then  the  formula  enables  us  to  obtain  ratios  of 
values  for  the  CH+  as  we  pass  from  one  concentration  of  acid  to  another, 
for  letting  ex  represent  the  pole  potential  corresponding  to  concentration 
of  hydrogen  ion  Cj  ,  and  e2  and  c2  have  a  similar  significance  with  respect 
to  another  concentration  we  have 

e±  —  e2  =  .000198  'T  log.  c± 


or  _L  =  10  0.000198  T 


cx :  c2  : :  1 :  10  0.000198  T 
and  so  for  any  number  of  concentrations  we  would  have 


c± :  c2 :  c3  :  .  .  .  cn    : :  1 :  10  0.000198  T  :  10  0.000198  T  :-...:  10  0.000198  T 

To  convert  these  ratios  into  absolute  values  it  is  only  necessary  to  know 
the  concentration  of  hydrogen  ion  corresponding  to  any  one  of  the  par- 
ticular concentrations  of  acid.  Before  proceeding  by  this  method,  how- 
ever, to  get  ratios  of  CH+  as  well  as  absolute  values  for  various  concen- 

iZ.  Physik  Ch.  4,  129  (1889). 


20 


trations  of  hydrochloric  acid  it  will  be  advantageous  to  construct  a  table, 
X,  for  hydrochloric  acid  at  25°  giving  the  CH+  as  determined  by  the 
Archenius  method  of  conductivity  ratios  : 


TABLE  X 

Cone.  HC1  0.1  0.01  0.001  0.0001         0.00001       0.000001 

C,  (.Conductivity)       0.092041     0.09518-     0.000991  »     .04993*     0.0.996*     0.0999* 


G 


Proceeding  now  by  means  of  Nernst's  formula  to  get  values  for  the 
ratios  of  CH+  after  the  manner  just  described,  we  obtain  from  the  data  of 
the  first  two  columns  of  Table  IV  the  folowing  results  for  HC1  at  25°. 

TABLE    XI 

Cone.  HC1  0.1  0.01  0.005  0.001  0.0001  0.00005 

RatiosH+  1  .114  .0606  .0126  .00121  .000586 

Cone.  HC1  0.00002  0.00001  0.0000005  0.000001 

RatiosH+  .000212  .0000803  .0000267  .0.287 

Next  taking  as  a  reference  value  the  figure  0.09204  for  the  concentration 
of  hydrogen  ion  in  0.1  M.  HC1  at  25°  (cf  Table  X)  we  get  as  values  for 
the  concentration  of  hydrogen  ion  in  hydrochloric  acid  those  which  have 
already  been  given  in  the  third  column  of  Table  IV.  At  this  point  it  must 
be  accentuated  that  the  absolute  values  which  are  obtained  for  the  C^ 

M"1" 

by  the  preceding  method  depend  upon  which  concentration  of  hydrogen 
ion,  evaluated  by  means  of  conductivity  ratios,  we  select  as  reference 
standard.  Thus  if  we  take  as  our  standard  the  figure  0.000991  for  the 
concentration  of  hydrogen  ion  in  0.001  M.  HC1  (Table  X)  we  get  as 
values  for  the  concentration  of  hydrogen  ion  for  hydrochloric  acid,  those 
given  in  Table  XII  and  which  on  an  average  differ  by  about  17%  from 
those  given  in  Table  IV. 

This  discrepancy  points  to  a  certain  inconsistency  between  Nernst's 
formula  and  the  Arrhenius  method  of  conductivity  ratios,  because  if  the 

1  Cf.  Fales  and  Vosburgh. 

2  Calculated  for  25°  from  the  conductivity  data  of  Noyes  (loc.  cit.  p.  137)  by 
use  of  the  method  of  least  squares  and  the  equation  A  25°  =  a  -f  bo  +  co2,  where 
a  is  the  equivalent  conductivity  at  18°  o,  is  the  temperature  difference  25°  —  18°, 
and  a,  b  and  c  are  constants  for  each  case.     For  zero  concentration  HC1,  a  =  379, 
b  =  6.651,  c  =  —  0.0111;    for  0.01  M.  HC1,  a  =  368, 

b  —  5,270,  c  =  —  0.0114. 

3  Kendall,  J.  Amer.  Chem.  Soc.  39,  7  (1917). 

1        1 

4  Extrapolated    values     obtained    by    extrapolating    the     function    —  =  --  \- 

A       Ao 
K(CA)°-*<>  . 


21 

TABLE   XII 

Cone.   HC1  0.1  0.01  0.001  0.0001          0.00001      0.000001 

C  H+   (e.m.f.)  .0779      0.00876      0.000959      0.000093      0.0.599      0.0622 

two  were  strictly  consistent  it  would  make  no  difference  in  the  absolute 
values  which  CH+  from  Table  X  was  taken  as  reference. 

Another  way  of  showing  this  inconsistency  is  to  calculate  the  value 

CH* 

of  K  in  the  formula  e  =  .000198  T  log ,  using  for  CH+  the  values 

KVpH2 

given  by  conductivity  ratios  (Table  X),  if  inconsistency  exists,  the  values 
for  K  will  not  be  constant.1 

Performing  the  necessary  calculations  with  the  aid  of  data  for  e  from 
Table  IV  we  obtain  the  results  given  in  Table  XIII  which  plainly  show 
the  variation  in  the  values  of  K,  and  particularly  that  the  variation  is  the 
greatest  in  the  regions  where  the  Arrhenius  method  of  conductivity. ratios 
must  resort  to  extrapolation. 


TABLE  XIII 

CH+  e 

Cone.  HC1  Conductivity  volts                          K 

0.1   Normal  0.09204  0.2166  10-4-70 

0.01  .009518  .1609  10-4-74 

.001  .000991  .1031  10-4-77 

.0001  0.0000993*  .0422  10-4-71 

.00001  0.0.996*  —.0255  10-4--7 

.000001  0.0a999*  —.1090  10-4-20 

*  extrapolated  values 

Proceeding  similarly  for  the  cases  of  acetic,  sulphuric,  and  phos- 
phoric acids,  we  get  by  aid  of  data  for  e  from  Tables  V,  VI  and  VII  the 
results  given  in  Table  XIV  ;  wherein  it  is  to  be  further  pointed  out  that 
the  K's  are  of  quite  a  different  order  of  magnitude  from  those  of  Table 
XIII. 


is,  J.  A.  C.  S.  35,  24  (1913)  discusses  this  point  and  says  with  reference  to 

RT         CH+ 
the  form  of  Nernst's  formula  which  he  employed,  namely,  E  =  EQ  --  In  -  , 

F 


where  EQ  corresponds  to  our  K  that  "Unless  the  concentration  of  the  hydrogen  ion 
is  exactly  proportional  to  the  activity,  the  value  of  EQ  calculated  from  this  equation 
will  not  be  constant,  but  in  any  case  it  will  approach  a  constant  value  as  the  con- 
centration approaches  zero." 


22 

TABLE   XIV 

Cone.  HC2H3O2  Conductivity1  volts  K 

0.05  Normal  0.000964  0.1056  10-4-80 

.005  .000311  .0771  KM-so 

.001  .000127  .0550  10-4-82 

Conc.H2SO4 

0.1  Normal  0.107-'  0.2092  lO-4-5* 

.01                                         .0157  •  .1568  10-4-4G 

.001                                       .00189  .1011  10-*-43 

Cone.  H3PO4 

0.1   Normal  0.0731  *  0.1684  10--»9 

.01                                         .0177  .1283  10-3-92 

.001                                       .00267  .0749  10-3-84 

There  are  several  possibilities  which  suggest  themselves  in  the  way  of 
explanations  as  to  the  inconsistency  between  the  results  arrived  at  by  the 
Arrhenius  method  of  "conductivity  ratios  and  the  e.m.f.  method  of  Nernst, 
and  without  wishing  to  favor  any  particular  hypothesis  or  to  draw  any 
positive  conclusions,  the  author  would  like  to  advance  certain  reflections 
which  seem  pertinent. 

If  the  manifestations  which  are  being  respectively  measured  by  the 
two  methods  belong  to  the  same  entity  then  it  would  appear  probable 
that  the  e.m.f.  method  because  of  its  basic  premise  that  the  gas  laws  apply 
to  solutions  should  give  results  in  close  agreement  with  the  conductivity 
method  only  when  we  are  concerned  with  electrolytes  which  follow  the  law 
of  mass  action ;  further  experimental  work  will  be  done  to  test  this  idea. 

If  the  manifestations  belong  to  different  entities  then  the  problem 
becomes  more  complicated.  A  possibility  along  this  line  of  reasoning  is 
that  in  aqueous  solution  of  electrolytes  we  are  dealing  not  with  simple 
ions  but  with  an  equilibrium  between  water,  hydrated  and  non-hydrated 
ions  and  that  the  conductivity  method  measures  both  kinds  of  ions  while 
the  e.m.f.  method  measures  only  the  unhydrated.  On  this  premise  we 
would  have  for  the  equilibrium  between  the  water  and  the  two  kinds  of 
ions  the  relationship 

nH2O  +  H+  ^  H+  (nH20)  3 

and  accordingly  as  we  go  toward  infinite  dilution  the  fraction  of  unhy- 
drated ion  would  approach  zero  as  a  limit  while  the  fraction  of  hydrated 
ion  would  approach  unity.  This  idea  seems  to  be  in  harmony  with  the 

iDerived  from  data  of  Kendall,  J.  C.  S.  101,  1283  (1912). 

2  Derived  from  data  of  Noyes  for  25°  Car.  Pub.  63,  262  (1907). 

3  n,  the  number  of  mols  of  water  entering  into  solvation  would  vary  with  dilu- 
tion.   For  a  resume  of  ideas  on  the  hydration  of  ions,  see  Kendall,  Proc.  Nat.  Acad. 
Sci.,  7,  56  (1921)  No.  2. 


23 

fact    that   the    ionized    fraction    of    an    acid,    as    determined    by    e.m.f. 
approaches  zero. 

Impurities 

The  impurities  to  be  considered  are  those  derived  as  follows :  (a) 
from  the  original  acids,  (b)  from  the  water,  (c)  from  the  solvent  action 
of  the  solutions  upon  the  glass  of  the  containing  stock  bottles  which  were 
all  of  "Non-sol"  glass,  (d)  from  the  solvent  action  of  the  solutions  upon 
the  glass  of  the  hydrogen  electrode  vessels  which  were  made  of  lime 
glass,  (e)  from  contact  of  the  solutions  with  the  air  during  the  opening 
of  bottles  and  the  operation  of  transferring  from  one  vessel  to  another. 

With  respect  to  these  several  captions  we  have :  (a)  the  impurities  in 
the  original  acids  would  at  most  only  constitute  a  minute  fractional  part 
of  the  acids  and  while  the  ratio  of  impurity  to  acid  would  remain  con- 
stant as  we  passed  from  one  dilution  of  acid  to  another,  the  absolute 
amount  of  impurity  would  be  becoming  infinitesimally  small,  conse- 
quently the  effect  of  such  impurities  may  be  considered  zero ;  (b)  the 
water  as  freshly  distilled  and  collected  had  an  ammonia  content  of 
0.5  mg.  NH3  per  liter,  which,  expressed  in  terms  of  molarity,  is  3  X  10-8 
mol  per  liter.  The  form  in  which  this  was  present  is  not  determinable, 
but  from  previous  remarks  x  we  will  assume  that  it  existed  as  ammonium 
carbonate  in  combination  with  carbon  dioxide  from  (e).  The  effect  of 
such  a  small  concentration  of  (NH4)2CO3  would  be  negligible  except 
perhaps  for  the  very  smallest  concentrations  of  acids  employed,  say  con- 
conerations  less  than  10-fi  M.  (c)  Conductivity  measurements  showed  no 
change  in  the  specific  conductivity  of  the  solutions  upon  standing  in  the 
"Non-sol"  bottles ;  this  effect  may  be  considered  zero ;  (d)  conductivity 
measurements  showed  an  appreciable  change  in  the  specific  conductivity 
of  the  solutions  during  the  first  sixty  minute  period  following  their  intro- 
duction into  the  hydrogen-electrode  vessel  and  then  no  further  appreci- 
able change;  the  e.m.f.  measurements  during  the  same  period  showed  no 
change ;  it  would  seem  reasonable,  therefore,  to  regard  this  effect  as 
negligible,  (e)  From  the  work  of  Kendall  -  it  seems  probable  that  all  the 
solutions  measured  would  have  a  CO2  content  of  about  1.4  X  10-5  M., 
which  is  that  corresponding  to  the  concentration  of  CO2  normally  present 
in  the  air ;  the  concentration  of  hydrogen  ion  due  to  this  CO2  is  not 
directly  measureable  because  of  the  repressant  action  of  the  hydrogen 
ion  from  the  particular  acid  under  examination,  namely  hydrochloric, 
acetic,  etc.  In  any  event,  it  is  not  likely  that  the  concentration  of  hydro- 
gen ion  contributed  by  the  CO2  in  the  presence  of  any  of  the  other  acids 

1  See  foot-note  under  caption  headed  "Preparation  of  Materials  and  Solutions." 

2  Above 


24 

could  be  greater  than  that  contributed  in  their  absence,  and  this  latter- 
concentration  was  found  to  be  1.1  X  10-7  M. ;  we  may  accordingly  neglect 
the  effect  of  the  CO2  except  perhaps  for  the  smallest  concentrations  of 
acids  measured,  say  1  X  10-6  M.  or  less,  and  even  here  the  corrections 
would  not  materially  affect  the  order  of  results  found  without  applying 
any  correction. 
Conclusions 

I.  Evidence  has  been  presented  to  show  that  the  degree  of  ionization 
of  the  acids  hydrochloric,  acetic,  sulphuric  and  phosphoric  as  determined 
by  measurements  of  their  hydrogen  ion  concentrations  by  the  electro- 
motive force  method  of  Nernst  goes  through  a  maximum  and  approaches 
zero  as  the  dilution  is  indefinitely  increased. 

II.  Certain    aspects    of    the   theory    underlying  the  two  principal 
methods  now  in  use  for  determining  the  degree  of  ionization  of  elec- 
trolytes, that  of  conductivity  ratios  and  that  of  electromotive  force  meas- 
urements, are  discussed  in  the  light  of  the  experimental  facts  advanced. 


VITA 

Harold  E.  Robertson  was  born  in  Rush  Center,  Kansas,  October  15, 
1897.  He  received  his  education  in  various  public  schools  in  that  state, 
graduating  from  Macksville  High  School.  He  received  his  bachelor's 
degree  from  Southwestern  College,  Winfield,  Kansas,  in  1918.  During 
the  winter  of  1917-18  he  was  chemistry  assistant  and  took  graduate  work 
at  Purdue  University,  Lafayette,  Indiana.  He  came  to  Columbia  Univer- 
sity in  January,  1919,  where  he  has  taken  graduate  work  and  assisted 
since  September,  1919. 


Lansine-Broas  Print, 

229-233  Union  St., 

Poughkeepsie,  N.  Y. 


BB10W 


nros. 
Makers 
Syracuse,  N.  Y. 

PAT.  JAN  21,  1908 


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